NIntegrate bug in Mathematica 6?

*To*: mathgroup at smc.vnet.net*Subject*: [mg84168] NIntegrate bug in Mathematica 6?*From*: vlad <volodymyr.babich at gmail.com>*Date*: Wed, 12 Dec 2007 05:12:50 -0500 (EST)

The following code in Mathematica 6: Clear[logdist1, pdfLog1, \[Mu]1, \[Sigma]1] logdist1 = LogNormalDistribution[(\[Mu]1 - \[Sigma]1^2/2), \[Sigma]1]; pdfLog1[x_] := PDF[logdist1, x] \[Mu]1 = 0.05; \[Sigma]1 = 0.2; NIntegrate[Min[100, 100 b1]*pdfLog1[b1], {b1, 0, 5}] NIntegrate[Min[100, 100 b1]*pdfLog1[b1], {b1, 0, 500}] NIntegrate[Min[100, 100 b1]*pdfLog1[b1], {b1, 0, 10000}] NIntegrate[Min[100, 100 b1]*pdfLog1[b1], {b1, 0, +\[Infinity]}] Produces the following output: 94.1407 38.1789 38.1789 94.1407 Note that the first and the last integrals have upper bounds of 5 and \ [Infinity] The middle ones have bounds 500 and 10000 All of the answers should be the same (we are way in the tail of the random variable density). I get no warnings or errors. Shouldn't Mathematica send me some warning that it has difficulty with convergence? Can I get Mathematica to send me a warning? If not, can I trust the numerical integration routines? Incidentally, Mathematica 5.2 give the correct answer of 94.1407 in all four cases.